[Feature]: Native /clear — fresh context in the same thread, like Claude Code

[bathan]

Problem

There is no way to start over inside a thread. To get a clean context and a clean
scrollback I have to settle the thread and create a new one, which means a new
title, re-picking model/mode, and losing the "place" I was working in.

Claude Code in the terminal has /clear: one command, the transcript is gone, and
I am in a fresh conversation in the same working directory. In T3 the equivalent
takes several UI steps and produces a pile of settled threads.

Current behavior

/clear is not a T3 command, so it is forwarded to the provider as plain text.
The model usually replies that the context was cleared, but nothing changed — see
#7402, where the event log shows /clear persisted as an ordinary
thread.message-sent followed by a normal turn. The assistant answering "done"
while keeping everything is worse than an error.

Proposal

Make /clear a native T3 command (alongside /model and /plan):

• Start a fresh provider session for the thread (no resume cursor, no transcript).
• Collapse or hide the previous messages in the thread view — a divider such as
  "Context cleared" is enough; the old messages can stay retrievable.
• Keep thread id, title, project, worktree, model selection, and permission mode.
• Until this exists: reject /clear (and other unsupported reset commands) with a
  visible "not supported" message instead of sending them to the model.

Why

Long-lived threads pinned to a worktree are the natural unit of work in T3; being
able to reset context without abandoning the thread keeps the sidebar sane and
matches what every provider CLI already offers.

[LukasFB]

+1, we need a function like that. I've been missing this in Codex since switching over from CC too.

Alternative approach with the same result: A function "Settle & start new task"
-> Settles the current task
-> Creates a new task with the same UI (repo, model, sidebar status, browser tabs, ...) but a fresh context

This would simplify this feature to just UI work inside T3, without any provider specific logic, since codex app-server does not have /clear support